Should we sample a time series more frequently? Decision support via multirate spectrum estimation (with discussion).

Suppose we have a historical time series with samples taken at a slow rate, e.g. quarterly. This article proposes a new method to answer the question: is it worth sampling the series at a faster rate, e.g. monthly? Our contention is that classical time series methods are designed to analyse a series at a single and given sampling rate with the consequence that analysts are not often encouraged to think carefully about what an appropriate sampling rate might be. To answer the sampling rate question we propose a novel Bayesian method that incorporates the historical series, cost information and small amounts of pilot data sampled at the faster rate. The heart of our method is a new Bayesian spectral estimation technique that is capable of coherently using data sampled at multiple rates and is demonstrated to have superior practical performance compared to alternatives. Additionally, we introduce a method for hindcasting historical data at the faster rate. A freeware R package, regspec, is available that implements our methods. We illustrate our work using official statistics time series including the United Kingdom consumer price index and counts of United Kingdom residents travelling abroad, but our methods are general and apply to any situation where time series data are collected.